Management Science I

Syllabus

1. Quantitative approach to management Introduction to the relationship between management and operations research, including the role of mathematical models and methods in economic decision-making. Classification of standard models and methods and the stages of solving optimization problems. Overview of the mathematical apparatus required for basic operations research models. 2. Structural models of the enterprise Explanation of the structure and components of enterprise models, focusing on internal and external resource flows. Definition and interpretation of direct and total consumption coefficients. Application of structural models in analyzing production and economic processes. 3. Optimization methods for enterprise management Introduction to mathematical programming tasks and their use in managerial decision-making. Fundamentals of linear programming and formulation of LP problems from real economic situations. Overview of geometric solution methods and interpretation of feasible and optimal solutions. 4. Solving linear programming problems using the simplex method Detailed explanation of the simplex method and its computational logic. Construction and use of simplex tableaux, pivot operations and identification of optimal solutions. Discussion of infeasible, unbounded and alternative optimal solutions. 5. Duality in linear programming problems Presentation of duality theory and its relationship to primal problems. Formulation of the dual problem, complementary slackness and interpretation of shadow prices. Economic meaning of duality in resource allocation and decision-making. 6. Sensitivity analysis of the optimal LP solution Methods for examining how changes in parameters affect the optimal solution. Interpretation of sensitivity intervals, allowable ranges and stability of optimal plans. Use of sensitivity analysis in economic evaluation and managerial decisions. 7. Transportation problems and their properties Overview of transportation models and their applications in logistics, distribution and supply chain management. Formulation of balanced and unbalanced transportation problems. Analysis of their mathematical structure and typical solution approaches. 8. Assignment problems and their solution Characteristics of assignment tasks and their importance in optimizing personnel, scheduling and production operations. Solution using the Hungarian method and related algorithms. Interpretation and practical use of the obtained assignments. 9. Basic types of network analysis problems Introduction to network models and their role in planning and optimization. Relation between network analysis and linear programming. Solving shortest-path problems and other typical network optimization tasks. 10. Critical path determination – CPM and PERT methods Principles of project network analysis, including activity times, floats and precedence relations. Deterministic CPM and probabilistic PERT approaches to project duration estimation. Application in project planning, scheduling and managerial decision-making. 11. Inventory modelling Classification of inventory models and their use in optimizing supply and stock levels. Overview of deterministic inventory models, both with and without shortages. Analysis of optimal order quantities and cost-minimization strategies. 12. Modelling of service (queueing) processes Introduction to queueing theory, its key concepts and performance metrics. Examination of basic models: no-waiting systems, waiting systems, single-channel and multi-channel queues. Understanding their behaviour and implications for system performance. 13. Optimization of service processes Methods for improving service system efficiency based on queueing models and performance indicators. Optimization of service capacities, waiting times and resource allocation. Application of these models in real managerial and operational decision-making.